{
  "id": 2351,
  "curve_key": "12870921321241:-45036309032099054461",
  "ainvs": [
    "1",
    "0",
    "1",
    "-268144194193",
    "52125335330691056"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 90.55797516511916,
  "faltings_height": 5.452320242595681,
  "conductor": "1074902010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "53"
  ],
  "discriminant": "60147927617060698492948533680062500",
  "regulator": "5.418240140522622952063117390157930661825",
  "points": [
    [
      "-593480",
      "47509007"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=19; A=(3q-p)(p+q)^3=-307125, B=-(p+3q)(p-q)^3=3424171. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 19:56:10",
  "updated_at": "2026-09-26 19:56:10"
}